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2 Answers
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This is more an anthropology question than psychology. Counter cultures and cults definitely are against mainstream society.

In America during the 60s there was a counter culture revolution. People found ideas from other cultures or invented cultural ideas and tried to bring them into mainstream. We called them all hippies at that time but now they are just ordinary people because their cultural revolution was largely popularized. People primarily associate hippies with a leftist movement but the Jesus freaks or Jesus movement was the equivalent in the religious conservative realm. Jesus freaks moved outside the realms of ordinary church. They were fundamentalist but spawned a diverse set of beliefs. The Jesus movement was also absorbed into mainstream culture and these two polar groups are a large reason why American belief systems are polarized between left and right in certain demographics at the moment.

Cults aggrandize a certain person, group of people or idea above family, government and the typical place of religion. I lived in Texas for a while so the first example that comes to my mind is Waco's Koresh who formed the group that was destroyed at their compound by the Clinton administration. He had a messiah complex mixed with some kind of hypersexualism. He was very charismatic and drew many people into his group with his pazazz. The of course the oft rumoured but very oft not found fundamental mormons which allow their people to be polygamist but god forbid any of those women ask to do polyandry. Putting a leader of a mormon church breakaway in jail became a national priority because in addition to the the polygamy there was incest in his groups.

Subcultures tend to be inside the realms of mainstream but hold to specific values that set the distinct. This might include the cowboy subculture, city dweller, yankee and southerner, various sexuality types, religious in various degrees and types. Freud had an interesting view that I've chosen to cherish his idea was like don't let yourself be defined by your sexuality (or other characteristic) instead embrace being human and all that it means.

Indeed people are drawn into counter-cultures outside of mainstream sometimes for positive and negative reasons. In general disenfranchisement by mainstream policies or values tends to lead people into depressive states which allows them to make atypical decisions to escape the pain of sadness. Oft people are drawn into cults by the charisma and happiness offered by the cult head or central idea. People tend to be born into subcultures and then choose to remain or seek out another group.

n.
One who attacks and seeks to overthrow traditional or popular ideas or institutions.

The previous answer covers various forms of reasoning on a larger scale. It can also be something much simpler, like being burned by popular trends, or finding that mainstream culture doesn't suit you (more unique individuals, etc).